3t 3x 3y 

 where 



9S^3U^3V^p (3_79) 



r 2 f 2 f 



M =1 u dz; M, , = I V dz; M = | uvdz 



a:x j^ yy i^ ^y l^ 



S S 



I udz; V = I v'iz; 

 ^d -d 



The symbols are defined as 



U , V = X and y components, respectively, of the volume 

 transport per unit width 



t = time 



Kj^p, Mj,;,, Mj-y = momentum transport quantities 



f = 2(1) sin (|) = Coriolis parameter 



0) = angular velocity of earth (7.29 x 10 radians 

 per second) 



(j) = geographical latitude 



g = gravitational acceleration 



E, = atmospheric pressure deficit in head of water 



C = astronomical tide potential in head of water 



T<,„ , T = X and y components of surface wind stress 

 sec sy 



Tr Ti = X and y components of bottom stress 



p = mass density of water 



W„ , W = X and y components of winds peed 

 X y 



u , v = X and y components, respectively, of current 

 velocity 



P = precipitation rate (depth/time) 



Equations (3-77) and (3-78) are approximate expressions for the equations 

 of motion, and equation (3-79) is the continuity relation for a fluid of 

 constant density. These basic equations provide, for all practical purposes, 

 a complete description of the water motions associated with nearly horizontal 

 flows such as the storm surge problem. Since these equations satisfactorily 

 describe the phenomenon involved, a nearly exact solution can be obtained only 

 by using these relations in complete form. 



It is possible to obtain useful approximations by ignoring some terms in 



3-121 



